The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
• Scale and Translation Model: If only GCPs are em 
ployed without redundancy, their distribution affects plane ac 
curacy greatly mainly because the calculation error by the small 
denominator during solution. Rotation of the coordinates by 45 
degrees can solve this problem and get stable solutions. Stan 
dardization is employed in the calculation to convert all the in 
put data between -0.5 and 0.5, which can reduce the calculation 
error caused by big difference of data. The plane accuracy is 2 
m to 5 m with 2 m for the best, while height accuracy is within 
0.6 m. Increase of GCP number does not count much when the 
number is more than 6. 
• Affine Model: At least 4 GCP are needed in affine 
model, and adjustment is needed when the GCP are redundant. 
Results with only 4 GCP are not stable. When GCP number is 
more than 8, accuracy is not sensitive to the GCP number. 
About 0.7 m in plane direction can be achieved when 16 well 
distributed GCP are employed, and the height accuracy is about 
0.5 m. 
• Second-order Affine Model: 10 GCP are needed for 
the model, and this is the most unstable model. One cannot get 
stable solutions when the GCP is 10, 12, 14, respectively, which 
means it has high requirement for GCP distribution. For this 
model, if the square items of height in plane direction equations 
are omitted (Equation 8.), the solution would be more stable, 
the right figure is the result of this simplified model. We can 
learn from the figure that for this model, with 16 well distrib 
uted GCP, the plane accuracy is within 0.6 m, and height accu 
racy is also within 0.6 m. 
P = Qq + o^X + + q 3 Z + q 4 XY + a 5 XZ + YZ + a 2 X + q%Y 
■ L = b 0 + b x X + b 2 Y + b 3 Z + b 4 XY + b 5 XZ + b 6 YZ + b,X 2 + b e Y 2 
H = c 0 + c t X + c 2 Y + c 3 Z + c 4 XY + c 5 XZ + c 6 YZ + c n X 2 + c s Y 2 + c 9 Z 2 
Figure 6. Figures of Accuracy with different GCP Number in image space: 
(a) .translation model; (b) scale and translation model; (c) affine model; (d) second-order affine model. 
3.3.2 Accuracy improvement in image space 
• The translation model is the simplest model and the 
minimum GCP number is 1. Providing one GCP, the accuracy 
is about 3 meters in plane direction and 4.5 meters in height di 
rection. Accuracy improves when more GCPs are available. 
With 6 or more GCPs available, accuracy in both directions are 
stable, about 2.2 m in Plane direction and 3.2 m in height direc 
tion can be achieved. The accuracy in latitude direction is much 
better than that in longitude direction. High accuracy can be ob 
tained when the GCPs are in the middle of the test region. 
• The minimum GCP number for translation and scale 
model is 2 and iterative calculation is needed for the solution of 
this model. When 2 GCPs are used in this model without redun 
dancy, accuracy is about 6 meters in plane direction and 16 me 
ters in height, thus for this model redundancy is necessary. With 
the increase of GCP number, accuracy in plane direction can 
achieve about 1 meter. With more than 8 GCPs, the accuracy in 
plane direction can be less than 1 m, up to about 0.85 m, and 
the height direction is about 1 meter. The maximum error in 
plane direction is about 2.5 meter and slightly less than that in 
height direction which is about 2.7 meter. 
• 3 GCPs are necessary for the affine model with itera 
tion needed for the solution. However, accuracy is also not sat 
isfying when only 3 GCPs are used in this model without re 
dundant number. With one more GCP, the accuracy is much 
better, about 1 meter in plane direction and 1.5 meter in height